Abstract

We have theoretically investigated the combined fundamental-mode and polarization selection in 850-nm oxide-confined vertical-cavity surface-emitting lasers (VCSELs) using a locally etched sub-wavelength surface grating. The physical mechanisms behind the selection are, first, the strongly polarization sensitive effective refractive index of the volume occupied by the grating structure, and second, the dramatic change of the reflectivity of a multi-layer Bragg mirror that can occur by simply changing the refractive index of the outermost layer. For a VCSEL cavity this layer is the surface layer and its refractive index is changed by the introduction of the sub-wavelength grating; in this case the grating leads to a higher reflectivity for the desired polarization. By localizing the surface grating area to a carefully chosen region near the optical axis it is therefore possible to ensure that the fundamental mode experiences a high reflectivity, or low cavity loss, while other modes experience more of the low-reflectance region of the peripheral part of the Bragg mirror and thus suffer higher loss. Cold-cavity calculations on a VCSEL with oxide aperture and grating region diameters of 4.5 μm and 2.5 μm, respectively, indicate that a loss difference of ~20 cm-1 between the fundamental mode and the first higher order mode can be obtained simultaneously with an orthogonal polarization mode discrimination of >15 cm-1. Based on previous experience, these values should enable robust single-mode operation with only the desired polarization orientation. What is also important, for the lasing mode the introduction of a sub-wavelength grating has no detrimental effect, so its characteristics, such as threshold current, slope efficiency, and far-field profile are unaffected. Moreover, since the effective index is a result of an averaging over several sub-wavelength grating periods, it is fairly insensitive to the detailed shape of the grating grooves, which should relax the fabrication tolerances.

© 2005 Optical Society of America

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References

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  1. H. J. Unold, M. C. Riedl, S. W. Z. Mahmoud, R. Jäger, and K. J. Ebeling, �??Long monolithic cavity VCSELs for high singlemode output power,�?? Electron. Lett. 37(3), 178�??179 (2001).
    [CrossRef]
  2. D. Zhou and L. J. Mawst, �??High-power single-mode antiresonant reflecting optical waveguide-type vertical-cavity surface-emitting lasers,�?? IEEE J. Quantum Electron. 38, 1599�??1606 (2002).
    [CrossRef]
  3. �?. Haglund, J. S. Gustavsson, J. Vukuši�?, P. Modh, and A. Larsson, �??Single fundamental mode output power exceeding 6 mW from VCSELs with a shallow surface relief,�?? IEEE Photon. Techn. Lett. 16, 368�??370 (2004).
    [CrossRef]
  4. S. J. Schablitsky, L. Zhuang, R. C. Shi, and S. Y. Chou, �??Controlling polarization of vertical-cavity surface-emitting lasers using amorphous silicon subwavelength transmission gratings,�?? Appl. Phys. Lett. 69, 7�??9 (1996).
    [CrossRef]
  5. J.-H. Ser, Y.-G. Ju, J.-H. Shin, and Y. H. Lee, �??Polarization stabilization of vertical-cavity top-surface-emitting lasers by inscription of fine metal-interlaced gratings,�?? Appl. Phys. Lett. 66, 2769�??2771 (1995).
    [CrossRef]
  6. Y. Hong, R. Ju, S. Spencer, and K. A. Shore, �??Investigation of polarization bistability in vertical-cavity surface-emitting lasers subjected to optical feedback,�?? IEEE J. Quantum Electron. 41, 619�??624 (2005).
    [CrossRef]
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  8. K. D. Choquette and R. E. Leibenguth, �??Control of vertical-cavity laser polarization with anisotropic transverse cavity geometries,�?? IEEE Photon. Techn. Lett. 6, 40�??42 (1994).
    [CrossRef]
  9. K. Panajotov, R. Kotynski, M. Camarena, and H. Thienpont, �??Modeling of the polarization behavior of elliptical surface-relief VCSELs,�?? Opt. Quantum Electron. 37, 241�??252 (2005).
    [CrossRef]
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    [CrossRef]
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  12. M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon Press, Bath, Great Britain, 1970).
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Appl. Phys. Lett. (2)

S. J. Schablitsky, L. Zhuang, R. C. Shi, and S. Y. Chou, �??Controlling polarization of vertical-cavity surface-emitting lasers using amorphous silicon subwavelength transmission gratings,�?? Appl. Phys. Lett. 69, 7�??9 (1996).
[CrossRef]

J.-H. Ser, Y.-G. Ju, J.-H. Shin, and Y. H. Lee, �??Polarization stabilization of vertical-cavity top-surface-emitting lasers by inscription of fine metal-interlaced gratings,�?? Appl. Phys. Lett. 66, 2769�??2771 (1995).
[CrossRef]

Electron. Lett. (2)

H. J. Unold, M. C. Riedl, S. W. Z. Mahmoud, R. Jäger, and K. J. Ebeling, �??Long monolithic cavity VCSELs for high singlemode output power,�?? Electron. Lett. 37(3), 178�??179 (2001).
[CrossRef]

�?. Haglund, J. S. Gustavsson, J. Vukuši�?, P. Jedrasik, and A. Larsson, �??High-power fundamental-mode and polarization stabilized VCSELs using a sub-wavelength surface grating,�?? Electron. Lett. 41(14), 37�??38 (2005).
[CrossRef]

IEEE J. Quantum Electron. (2)

D. Zhou and L. J. Mawst, �??High-power single-mode antiresonant reflecting optical waveguide-type vertical-cavity surface-emitting lasers,�?? IEEE J. Quantum Electron. 38, 1599�??1606 (2002).
[CrossRef]

Y. Hong, R. Ju, S. Spencer, and K. A. Shore, �??Investigation of polarization bistability in vertical-cavity surface-emitting lasers subjected to optical feedback,�?? IEEE J. Quantum Electron. 41, 619�??624 (2005).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

N. Nishiyama, M. Arai, S. Shinada, M. Azuchi, T. Miyamoto, F. Koyama, and K. Iga, �??Highly strained GaInAs-GaAs quantum-well vertical-cavity surface-emitting laser on GaAs (311)B substrate for stable polarization operation,�?? IEEE J. Sel. Top. Quantum Electron. 7, 242�??248 (2001).

IEEE Photon. Techn. Lett. (2)

K. D. Choquette and R. E. Leibenguth, �??Control of vertical-cavity laser polarization with anisotropic transverse cavity geometries,�?? IEEE Photon. Techn. Lett. 6, 40�??42 (1994).
[CrossRef]

�?. Haglund, J. S. Gustavsson, J. Vukuši�?, P. Modh, and A. Larsson, �??Single fundamental mode output power exceeding 6 mW from VCSELs with a shallow surface relief,�?? IEEE Photon. Techn. Lett. 16, 368�??370 (2004).
[CrossRef]

Opt. Commun. (1)

J. M. Ostermann, P. Debernardi, C. Jalics, A. Kroner, M. C. Riedl, and R. Michalzik, �??Surface gratings for polarization control of single- and multi-mode oxide-confined vertical-cavity surface-emitting lasers,�?? Opt. Commun. 246, 511�??519 (2005).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Opt. Quantum Electron. (1)

K. Panajotov, R. Kotynski, M. Camarena, and H. Thienpont, �??Modeling of the polarization behavior of elliptical surface-relief VCSELs,�?? Opt. Quantum Electron. 37, 241�??252 (2005).
[CrossRef]

Solid State Comm. (1)

M. A. Afromowitz, �??Refractive index of Ga1�??xAlxAs,�?? Solid State Comm. 15(1), 59�??63 (1974).
[CrossRef]

Vertical-Cavity Surface-Emitting Lasers (1)

D. Kuksenkov and H. Temkin, �??Polarization Related Properties of Vertical-Cavity Lasers,�?? in Vertical-Cavity Surface-Emitting Lasers, C. Wilmsen, H. Temkin, and L. A. Coldren, eds. (Cambridge University Press, Cambridge, U.K., 1999), pp. 233�??267

Other (1)

M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon Press, Bath, Great Britain, 1970).

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Figures (5)

Fig. 1.
Fig. 1.

(a) A sub-wavelength grating with period Δ and ridge width a, and its effective index equivalent for a plane wave propagating in the z-direction. (b) Effective index in GaAs as a function of duty cycle d=a/Δ at a free-space optical wavelength (λ 0) of 840 nm.

Fig. 2.
Fig. 2.

(a) Schematic illustration of the VCSEL structure and (b) an SEM image of a test grating with period 120 nm etched in bulk GaAs, with a lateral extent typical for a VCSEL with a surface grating.

Fig. 3.
Fig. 3.

(a) Cavity loss forE , (b) cavity loss for E , and (c) loss difference, loss for E -loss for E , as a function of grating etch depth and duty cycle.

Fig. 4.
Fig. 4.

(a) Modal loss as a function of grating duty cycle for a VCSEL with a 60-nm grating etch depth and (b) modal loss as a function of grating etch depth for a VCSEL with a 60% duty cycle. The oxide aperture is 4.5 μm and the grating region diameter is 2.5 μm.

Fig. 5.
Fig. 5.

Output power (polarization resolved) and OPSR versus current, optical spectra, and far-field, for a VCSEL with a sub-wavelength surface grating along (a) the [01̅1] direction, and (b) along the [011] direction. The oxide aperture diameter is 4.5 μm, the grating region diameter is 2.5 μm, the grating duty cycle is 60%, and the grating etch depth is 60 nm.

Equations (2)

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ε eff∥ = 1 + d ( ε 1 )
ε eff⊥ = ε d + ε ( 1 d ) ,

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